Problem: Multiply the following complex numbers: $({-2+2i}) \cdot ({5+5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2+2i}) \cdot ({5+5i}) = $ $ ({-2} \cdot {5}) + ({-2} \cdot {5}i) + ({2}i \cdot {5}) + ({2}i \cdot {5}i) $ Then simplify the terms: $ (-10) + (-10i) + (10i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -10 + (-10 + 10)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -10 + (-10 + 10)i - 10 $ The result is simplified: $ (-10 - 10) + (0i) = -20 $